How to display minimum spannign tree matrix - c++

Question

#include <algorithm>
#include <iostream>
#include <vector>
#include <queue>
#include<iomanip>
using namespace std;
typedef pair<int, int> intPair;// rename intPair
typedef vector<double> doubleVector; //rename doubleVetcor
typedef vector<intPair> intPairVector; // rename intPairVector
// Union-Find Disjoint Sets Library written in OOP manner, using both path compression and union by rank heuristics
class UnionFind { // OOP style
private:
doubleVector p, rank, setSize; // remember: vi is vector<double>
int numSets;
public:
UnionFind(int N) {
setSize.assign(N, 1);
numSets = N;
rank.assign(N, 0);
p.assign(N, 0);
for (int i = 0; i < N; i++)
p[i] = i;
}
int findSet(int i) {
return (p[i] == i) ? i : (p[i] = findSet(p[i]));
}
bool isSameSet(int i, int j) {
return findSet(i) == findSet(j);
}
void unionSet(int i, int j) {
if (!isSameSet(i, j)) {
numSets--;
int x = findSet(i), y = findSet(j);
// rank is used to keep the tree short
if (rank[x] > rank[y]) {
p[y] = x;
setSize[x] += setSize[y];
}
else{
p[x] = y;
setSize[y] += setSize[x];
if (rank[x] == rank[y])
rank[y]++;
}
}
}
int numDisjointSets() {
return numSets;
}
int sizeOfSet(int i) {
return setSize[findSet(i)];
}
};
vector<intPairVector> AdjList;
int main() {
int num_verts=0;
cin >> num_verts;
//Pre-allocate a vector of num_verts rows, each of which is a vector
//of num_verts copies of 0.0
vector<vector<double>> matrix(num_verts, vector<double>(num_verts,0.0));
//Requires c++11 or higher
for(int row = 0; row<num_verts;++row) {
for(int col = 0; col<num_verts; ++col){
cin >> matrix[row][col];
}
}
//print out the matrix we just read
for(int row = 0; row<num_verts; ++row) {
for(int col=0; col<num_verts;++col){
cout << setprecision(2) << fixed << matrix[row][col] << "\t";
}
cout << "\n";
}
// Kruskal's algorithm merged
AdjList.assign(num_verts, intPairVector());
vector< pair<double, intPair> > EdgeList; // (weight, two vertices) of the edge
for (int row = 0; row<num_verts; ++row) {
for(int col=0; col<num_verts;++col){
EdgeList.push_back(make_pair(matrix[row][col], intPair(row,col)));
AdjList[row].push_back(intPair(row,matrix[row][col]));
AdjList[col].push_back(intPair(col,matrix[row][col]));
}
}
sort(EdgeList.begin(), EdgeList.end()); // sort by edge weight O(E log E)
// note: pair object has built-in comparison function
double mst_cost = 0.0;
UnionFind UF(num_verts); // all V are disjoint sets initially
for (int i = 0; i < num_verts*num_verts; i++) { // for each edge, O(E)
pair<double,intPair> front = EdgeList[i];
if (!UF.isSameSet(front.second.first, front.second.second)) { // check
mst_cost += front.first; // add the weight of e to MST
UF.unionSet(front.second.first, front.second.second); // link them
}
} // note: the runtime cost of UFDS is very light
//display the weight of the MST
cout << setprecision(2) << fixed << mst_cost << endl;
return 0;
}
I am trying to display the minimum spanning tree from this code, I cannot figure out how to get this code to display the modified matrix. The code is working correctly, by that I mean it is compiling and calculating the correct weight for the graph. However, I am unsure how to display the minimum spanning tree from using Kruskals algorithm. Thanks for any help

Answer 1

Whenever you add the weight of an edge to the weight of the MST, you should also add that edge to a list to keep track of the MST edges.